1. EMT 110 Engineering Materials
Lecture 4:
Solidification and Crystalline Imperfection
Zulkarnain Mohamed Idris
Semester /2013

2. Solidification of Metals
Metals are melted to produce finished and semi- finished parts.
Two steps of solidification:
Nucleation : Formation of stable nuclei.
Growth of nuclei : Formation of grain structure.
Thermal gradients define the shape of each grain.
Grains
Nuclei
Crystals that will
Form grains
Grain Boundaries
Liquid
Figure 4.2
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3. Formation of Stable Nuclei
Two main mechanisms: Homogenous and heterogeneous.
Homogenous Nucleation :
First and simplest case.
Metal itself will provide atoms to form nuclei.
Metal, when significantly undercooled, has several slow moving atoms which bond each other to form nuclei.
Cluster of atoms below critical size is called embryo.
If the cluster of atoms reach critical size, they grow into crystals. Else get dissolved.
Cluster of atoms that are grater than critical size are called nucleus.
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4. Energies involved in homogenous nucleation.
Volume free energy, Gv
Released by liquid to solid transformation.
ΔGv is change in free energy per unit volume between liquid and solid.
Free energy change for a spherical nucleus of radius r is given by
Surface energy, Gs
Required to form new solid surface
ΔGs is energy needed to create a surface.
γ is specific surface free energy.
Then,
ΔGs is retarding energy.
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5. Total Free Energy Since when r=r*, d(ΔGT)/dr = 0
Total free energy is given by
Since when r=r*, d(ΔGT)/dr = 0
ΔGs +
Nucleus
ΔGT
Above critical
radius r*
Below critical
radius r* ΔG r r* r*
Energy
lowered by
growing into
crystals
Energy
Lowered by
redissolving -
Figure 4.4
ΔGv
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6. Critical Radius Versus Undercooling
Greater the degree of undercooling, greater the change in volume free energy ΔGv
ΔGs does not change significantly.
As the amount of undercooling ΔT increases, critical nucleus size decreases.
Critical radius is related to the amount of undercooling by the relation
r* = critical radius of nucleus
γ = Surface free energy
ΔHf = Latent heat of fusion
Δ T = Amount of undercooling.
Tm=Freezing Temperature in Kelvin
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7. Calculate the critical radius (in cm) of a homogeneous nucleus that forms when pure liquid copper solidifies. Assume T=0.2Tm, use data from Table 4.1, calculate the number of atoms in the critical sized nucleus at this undercooling .

8. Solution:

9. Solution:

10. Heterogenous Nucleation
Nucleation occurs in a liquid on the surfaces of structural material. E.g:- Insoluble impurities.
These structures, called nucleating agents, lower the free energy required to form stable nucleus.
Nucleating agents also lower the critical size.
Smaller amount of undercooling is required to solidify.
Used excessively in industries.
Liquid
Solid θ
Nucleating
agent
Figure 4.6
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11. Growth of Crystals and Formation of Grain Structure
Nucleus grow into crystals in different orientations.
Crystal boundaries are formed when crystals join together at complete solidification.
Crystals in solidified metals are called grains.
Grains are separated by grain boundaries.
The more the number of nucleation sites available, more the number of grains formed.
The number of nucleation sites will affect the structure of the solid metal produced.
If relative few nucleation sites are available, a coarse or large-grain structure will be produced.
If many nucleation sites are available, a fine-grain structure will result.
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12. Types of Grains Equiaxed Grains:
Crystals, smaller in size, grow equally in all directions.
Formed at the sites of high concentration of the nuclei.
Example:- Cold mold wall
Columnar Grains:
Long thin and coarse.
Grow predominantly in one direction.
Formed at the sites of slow cooling and steep temperature gradient.
Example:- Grains that are away from the mold wall.
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13. Types of Grains (Cont’)

14. Casting in Industries
In industries, molten metal is cast into either semi finished or finished parts.
Figure 4.9b
Continuous casting
Of steel ingots
Figure 4.8
Direct-Chill semicontinuous
Casting unit for aluminum
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15. Grain Structure in Industrial castings
To produce cast ingots* with fine grain size, grain refiners are added.
Example:- For aluminum alloy, small amount of Titanium, Boron or Zirconium is added.
*An ingot is a material, usually metal, that is cast into a shape suitable for further processing.
Al ingot
Grain structure of
Aluminum cast
with (b) and
without (a)
grain refiners.
(a)
(b)
Figure 4.10
4-11
After “Metals Handbook” vol. 8, 8th ed., American Society of Metals, 1973, p.164)

16. Solidification of Single Crystal
For some applications (Eg: Gas turbine blades-high temperature environment), single crystals are needed.
Single crystals have high temperature creep resistance.
Latent head of solidification is conducted through solidifying crystal to grow single crystal.
Growth rate is kept slow so that temperature at solid- liquid interface is slightly below melting point.
Figure 4.12
Growth of single
crystal for turbine
airfoil.
4-12
(After Pratt and Whitney Co.)

17. Solidification of Single Crystal
Silicon single crystal is another example of industrial use of single crystal.
Silicon single crystals are sliced into wafers for solid-state electronic integrated circuit chips.
Single crystals are necessary for this application since grain boundaries would disrupt the flow of electrons in the device made from semiconductor silicon.
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18. Solidification of Single Crystal
Different grain structures of gas turbine airfoil blades:
Polycrystal Equiaxed , (b) Polycrystal Columnar, and
(c) Single Crystal

19. Czochralski Process
This method is used to produce single crystal of silicon for electronic wafers*.
A seed crystal is dipped in molten silicon and rotated.
The seed crystal is withdrawn slowly while silicon adheres to seed crystal and grows as a single crystal.
*Electronic wafer: a thin slice of semiconductor material, such as a silicon crystal, used in the fabrication of integrated circuits and other microdevices.

20. Metallic Solid Solutions
Few metals that are used in pure or nearly pure state are like high purity copper in electronic wire and high-purity aluminum used for bright metallic surface.
Alloys are used in most engineering applications.
Alloy is an mixture of two or more metals and nonmetals.
Example:
Cartridge brass is binary alloy of 70% Cu and 30% Zinc.
Iconel is a nickel based superalloy with about 10 elements.
Solid solution is a simple type of alloy in which elements are dispersed in a single phase.
There are two types of solid solutions: substitutional and interstitial
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21. Substitution Solid Solution
Solute atoms substitute for parent solvent atom in a crystal lattice.
The structure remains unchanged.
Lattice might get slightly distorted due to change in diameter of the atoms.
Solute percentage in solvent
can vary from fraction of a
percentage to 100%
Solvent atoms
Figure 4.14
Solute atoms
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22. Substitutional Solid Solution (Cont..)
According to the Hume-Rothery rules, the solubility of solids is greater if
The diameter of atoms not differ by more than 15%
Crystal structures are similar.
No much difference in electronegativity (else compounds will be formed).
Have same valence.
Examples:-
System
Atomic radius
Difference
Electron-egativity difference
Solid
Solibility
Cu-Zn
3.9%
0.1
38.3%
Cu-Pb
36.7%
0.2
0.17%
Cu-Ni
2.3%
100%
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23. Interstitial Solid Solution
Solute atoms fit in between the voids (interstices) of solvent atoms.
Solvent atoms in this case should be much larger than solute atoms.
Example:- between 912 and 13940C, interstitial solid solution of carbon in γ iron (FCC) is formed.
A maximum of 2.8%
of carbon can dissolve
interstitially in iron.
Iron atoms r00.129nm
Carbon atoms r=0.075nm
Figure 4.15a
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25. Crystalline Imperfections
No crystal is perfect.
Imperfections affect mechanical properties, chemical properties and electrical properties.
Imperfections can be classified as
Zero dimension /point defects.
One dimension / line defects (dislocations).
Two dimension defects.
Three dimension defects (cracks).
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26. Point Defects – Vacancy
Vacancy is formed due to a missing atom.
Vacancy is formed (one in atoms) during crystallization or mobility of atoms.
Energy of formation is 1 ev.
Mobility of vacancy results in cluster of vacancies.
Also caused due
to plastic deformation,
rapid cooling or particle
bombardment.
Figure: Vacancies moving to form vacancy cluster
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27. Point Defects - Interstitially
Atom in a crystal, sometimes, occupies interstitial site.
This does not occur naturally.
Can be induced by irradiation.
This defects caused structural distortion.
Figure 4.16b
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28. Point Defects in Ionic Crystals
Complex as electric neutrality has to be maintained.
If two oppositely charged particles are missing, cation- anion divacancy is created. This is schottky imperfection.
Frenkel imperfection is created when cation moves to interstitial site.
Impurity atoms are
also considered as
point defects.
Figure 4.17
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29. Line Defects – (Dislocations)
Lattice distortions are centered around a line.
Formed during:
Solidification
Permanent Deformation
Vacancy condensation
Different types of line defects are:
Edge dislocation
Screw dislocation
Mixed dislocation
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30. Edge Dislocation Created by insertion of extra half planes of atoms.
Positive edge dislocation
Negative edge dislocation
Burgers vector
shows displa-
cement of
atoms (slip).
Burgers vector
Figure 4.18
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31. Screw Dislocation
Created due to shear stresses applied to regions of a perfect crystal separated by cutting plane.
Distortion of lattice in form of a spiral ramp.
Burgers vector is parallel to dislocation line.
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After M. Eisenstadt, “Introduction to Mechanical Properties of Materials,” Macmillan, 1971, p.118

32. Mixed Dislocation Most crystal have components of both edge and screw
Dislocation, since have
irregular atomic arrangement
will appear as dark lines
when observed in electron
microscope.
Figure 4.21
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33. Planar Defects
Grain boundaries, twins, low/high angle boundaries, twists and stacking faults
Free surface is also a defect : Bonded to atoms on only one side and hence has higher state of energy Highly reactive
Nanomaterials have small clusters of atoms and hence are highly reactive.

34. Grain Boundaries Grain boundaries separate grains.
Formed due to simultaneously growing crystals meeting each other.
Width = 2-5 atomic diameters.
Some atoms in grain boundaries have higher energy.
Restrict plastic flow and prevent dislocation movement.
Figure 4.25
3D view of
grains
Grain Boundaries
In 1018 steel
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(After A.G. Guy, “ Essentials of materials Science,” McGraw-Hill, 1976.)

35. Twin Boundaries
Twin: A region in which mirror image of structure exists across a boundary.
Formed during plastic deformation and recrystallization.
Strengthens the metal.
Twin Plane
Twin

36. Other Planar Defects and Volume Defects
Small angle tilt boundary: Array of edge dislocations tilts two regions of a crystal by < 100
Stacking faults: Piling up faults during recrystallization due to collapsing.
Example: ABCABAACBABC FCC fault
Volume defects: Cluster of point defects join to form 3-D void or pore.